How to add more light to the 3D view
I'm afraid there is no way to fully fix this issue, but you can help slightly. 

In file > User Preferences > System under "Solid OpenGL lights" (1) you can see three sets of colours (2). 


Editing all of these to a full white, (Clicking on each then adjusting the colour to the brightest white.) will help your issue.

EDIT: After viewing your edited post, i can say this is what my answer does. But like i said only to a extent. But, i have noticed, if normal's are pointing inside of a object, it is darker, the dark side of your object is unusual. 

Try selecting the darker side in edit view with faces selected, then hold down 'CTRL' and press 'N'  this recalculates the normals. Also another thing to try is checking them manually. To do this, press 'N' then while in edit mode scroll down until you see a section called normals. (1)


Then click on one of the three boxes, i prefer faces (2) for normal things, but sometimes it doesn't matter what you prefer.